Fermions in a stochastic medium

Abstract

We use our background field method to calculate the disorder averaged single-particle Green’s function of fermions subject to a time-dependent random potential with long-range spatial correlations. We show that bosonization provides a microscopic basis for the description of the quantum dynamics of an interacting many-body system via an effective stochastic model with Gaussian probability distribution. In the limit of static disorder our method is equivalent with conventional perturbation theory based on the lowest order Born approximation. We also critically discuss the linearization of the energy dispersion, and give a simple example where this approximation leads to an unphysical result. Some of the calculations described in this chapter have been published in [9.1].